So I found there can be drastic variations in how the war plays out between the occupying force and the invading force. Sometimes the Russians will steamroll them, sometimes they will get drive. Off the island.

As for the aggr stat, that's normal behavior. You can reduce aggr by healing wounded enemy soldiers, but this is tedious and doesn't make a huge affect. It is mainly a way to keep things quiet in the very early game. Once you start taking territory it will ramp up quickly.
The way the logic works, is every 10 minutes the game awards you your income, and also decides if it should launch a big attack. It will have to decide whether to attack you or the Russians. A good strategy is to be aggressive (at this point) and capture several points if you can. That way when they country attack, you might lose one area but if you captured 3 you are still up 2. Then make another big push before they work up their next attack.

But that's just the big attack. They will usually counter with what troops they can spare any time you take something. The small attacks usually consist of one squad of troops or one apc or similar. With the new version im releasing this week, these will scale a little better.

Also, you very well can knock out all of the enemies air assets, as well as their apcs so that their counter attacks will consist of infantry in trucks. So at the point you where when you made this post you are at about the hardest point in the game. If you stick it out and knock out a lot of their assets, they will weaken significantly.